YILDIZ Technical University Department of Mechanical Engineering Fluid Mechanics – Midterm -I- exam questions (G1) Name, Surname No 1- What is viscosity? What is the cause of it in liquids and in gases? Do liquids or gases have higher dynamic viscosities? Viscosity is a measure of the “stickiness” or “resistance to deformation” of a fluid. It is due to the internal frictional force that develops between different layers of fluids as they are forced to move relative to each other. Viscosity is caused by the cohesive forces between the molecules in liquids, and by the molecular collisions in gases. Liquids have higher dynamic viscosities than gases. 2- Consider two identical glasses of water, one stationary and the other moving on a horizontal plane with constant acceleration. Assuming no splashing or spilling occurs, which glass will have a higher pressure at the (a) front, (b) midpoint, and (c) back of the bottom surface? The pressure at the bottom surface is constant when the glass is stationary. For a glass moving on a horizontal plane with constant acceleration, water will collect at the back but the water depth will remain constant at the center. Therefore, the pressure at the midpoint will be the same for both glasses. But the bottom pressure will be low at the front relative to the stationary glass, and high at the back (again relative to the stationary glass). Note that the pressure in all cases is the hydrostatic pressure, which is directly proportional to the fluid height. 3- Two round, open tanks containing the same type of fluid rest on a table top as shown in Figure. They have the same bottom area, A, but different shapes. When the depth, h, of the liquid in the two tanks is the same, the pressure force of the liquids on the bottom of the two tanks is the same. However, the force that the table exerts on the two tanks is different because the weight in each of the tanks is different. How do you account for this apparent paradox? For the tank with the inclined walls the pressure on the bottom is due to the weight of liquid in the column directly above the bottom as shown the dashed lines in the figure. This is the same weight as that for the tank with the straight sides. Thus, the pressure on the bottom of the two tanks is the same. The additional weight in the tank with the inclined walls is supported by the inclined walls, as illustrated in the figure. 4- The pressure of water flowing through a pipe is measured by the arrangement shown in Figure. For the values given, calculate the pressure in the pipe. 8/12 0.6667 P !" 30 1000 ∙ 9.81 ∙ (0.50 2.4 ∙ 0.06 ∙ 0.6667 0.06 ∙ 0.6667,/1000 =33.6 kPa 5- A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B. Determine the hydrostatic force exerted on the gate by the 5-m-high water and the location of the pressure center. 336 61845 1000 9 9 3 3 67 8 2 3.71: 9 2 12(8 , 2 12(2 3, 2 2 ./ 0 1 2 1000 ∙ 9.81 ∙ 3.5 ∙ 22.11.2012 Prof. Dr. Ali PINARBAŞI YILDIZ Technical University Department of Mechanical Engineering Fluid Mechanics – Midterm -I- exam questions (G1) Name, Surname No 6- A 50x30x20-cm block weighing 150 N is to be moved at a constant velocity of 0.8 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be applied in the horizontal direction. (b) If a 0.4-mm-thick oil film with a dynamic viscosity of 0.012 Pa.s is applied between the block and inclined surface, determine the percent reduction in the required force. ∑ .< 0:. .>? cos 20 .C sin 20 0 F .G 0:.C cos 20 .>? sin 20 H 0 Friction force: Ff=fFN1 .C H 150 177.05 cos 20 I20 cos 20 0.2720 . .J cos 20 .C sin 20 (0.273177, cos 20 177 sin 20 105.55 M .>? K 1> L1> 0.012 ∙ ? (N.O<N.,N.P Q<NRS 2.45 F .< 0:. .>? cos 20 .C sin 20 0 F .G 0:.C cos 20 .>? sin 20 H 0 .C .>? sin 20 H (2.4 sin 20 150, 160.55 cos 20 cos 20 . .>? cos 20 .C sin 20 2.4 cos 20 160.5 sin 20 57.25 Percentage reduction in the required force: 22.11.2012 TURTV TU 100 NO.OWOX. NO.O 100 45.8% Prof. Dr. Ali PINARBAŞI